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42 Cards in this Set

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use the definition of factor to show that 3 is a factor of 15.

three is a factor of fifteen because there is a unique whole number namely five such that 3*5=15.

true or false problem solving strategy

try to find a counter example, if you cannot find one than it is true.

in the case that it contains "there exsists" or "it is possible to find".

only one statement makes it true

Divisibility of a sum theorem

if A divides B and A divides C than A divides B+C

Divisibility of a difference theorem

if A divides B and A divides C than A divides B-C

Divisibiliy of a product theorem

if A divides B than A divides BxC

Divisibility test for 2,5,and 10

2- only if the ones place ends in an even number


5- only if the ones place ends in a 5 or 0


10- only if the ones place ends in a 0

Divisibility test for 4 and 8

4- only if 4 divides the number formed by the two rightmost digits.



8- only if 8 divides the number formed by the three right most digits.

Divisibility test for 3 and 9

3- only if the sum of the digits is divisible by 3



9- only if the sum of the digits is divisible by 9

Divisibility test for 6

6- only if the number is divisible by both 2 and 3

what are the three steps in the factor list method

1) List all the postive factors of each number


2) List all the common positive factors


3) Identify the GCF

What are the four steps for The Prime Factorization Method

1)Use the factor tree method or the prime divisor method to find the prime factorization of each number.


2) Write the prime factorization of each numberlisting the factors in the product from smallest to largest without exponents.


3) Circle the prime factors that are common to


every mumber.


4) Multiply the commom prime factors to get


the GCF.

define the Euclidean Algorithm

you find the GCF of each set starting with the two numbers writhing the largest first and than deviding the largest number by the smallest, and repeting the process until you get to 0.

when two natural numbers have no common factors other than 1 they are said to be _______.

relatively prime

what are the three methods for finding the LCM

1) THE MULTIPLE LIST METHODS.


2) THE PRIME FACTORIZATION METHOD.


3) THE DEVISION BY PRIMES METHOD.

THE UNION OF THE SET OF WHOLE NUMBERS AND THE SET OF OPPOSITES (NEGITIVES) OF THE NATURAL NUMBERS IS CALLED THE SET OF ____.

INTEGER

THE SET OF POSITIVE NUMBERS IS _____ AND IS THE SAME AS THE SET OF NATURAL MUMBERS

1^+ = {1,2,3,...}

THE SET OF NEGATIVE INTEGERS IS ______ AND IS THE SAME AS THE SET OF OPPOSITES OF THE NATURAL NUMBERS.

1^- = {..., -3, -2, -1}

THE SET OF NONNEGATIVE INTEGERS IS ____ AND IS THE SAME AS THE SET OF WHOLE NUMBERS.

{0,1,2,3,...}

_______ CAN ALSO BE USED TO REPRESENT INTEGERS.

SIGNED COUNTERS

DEFINITION OF ABSOLUTE VALUE

IS THE DISTANCE FROM ZERO TO THE NUMBER LINE

INTEGER ADDITION CAN BE MODELED USING A ____ AND ____.

1) NUMBER LINE


2) SIGNED COUNTERS

A+B IS A UNIQUE INTEGER

CLOSURE PROPERTY OF ADDITION OF INTEGERS

A+B=B+A

COMMUTATIVE PROPERTY OF ADDITION OF INTEGERS

(A+B) C = A+(B+C)

ASSOCIATIVE PROPERTY OF ADDITION OF INTEGERS

A+0 = A = 0+ A

ADDITIVE IDENTITY PROPERTY OF INTEGERS

A + (-A) = 0 =-A+A

ADDITIVE INVERSE(OPPOSITES) PROPERTY OFINTEGERS

DEFINITION OF INTEGER SUBRACTION

A-B=A+(-B)

SUBTRACTING AN INTEGER IS THE SAME AS ADDING ITS _____

OPPOSITE

ANY SUBTRACTION PROBLEM CAN BE REWRITTEN AS AN ADDITION PROBLEM, WHAT ARE THE STEPS

1) READ THE PROBLEM


2) WHEN YOU READ "MINUS" SIMPY INSERT A PLUS SIGN IN FRONT OF IT


3) NOW REREAD THE PROBLEM AND COMPUTE THE SUM USING THE ADDITION RULES

CLOSURE PROPERTY OF ADDITION OF INTEGERS

A-B IS A UNIQUE INTEGER

the product of two positive integers is ----.
positive
the product of a positive integer and a negative integer is ----
negative
-1 times a number is the same as the --- of the number
opposite
the product of two negative integers is ---
positive
if a and b are integers with b note equalling 0, than a/b is a ----.
a unique integer
the quotient of two positive integers is ---.
positive
the quotient of a positive integer and a negative integer is ---.
negative
the quotient of two negative integers is ---.
positive
if a<b, then
a+b<b+c
if a<b and c> 0, then
a*c< b*c
if a<b and c<0, then
a*c >b*c